We introduce classes of differential susceptibility and infectivity epidemic models. These models address the problem of flows between the different susceptible, infectious and infected compartments and differential death rates as well. We prove the global stability of the disease free equilibrium when the basic reproduction ratio R0≤1 and the existence and uniqueness of an endemic equilibrium when R0>1. We also prove the global asymptotic stability of the endemic equilibrium for a differential susceptibility and staged progression infectivity model, when R0>1. Our results encompass and generalize those of Hyman and Li (J Math Biol 50:626-644, 2005; Math Biosci Eng 3:89-100, 2006).
We prove the existence and uniqueness of entropy solution for nonlinear anisotropic elliptic equations with Neumann homogeneous boundary value condition for 1 -data. We prove first, by using minimization techniques, the existence and uniqueness of weak solution when the data is bounded, and by approximation methods, we prove a result of existence and uniqueness of entropy solution.
We study the boundary value problemwhere Ω is a smooth bounded domain in R N (N 3) and div a(x, ∇u) is a p(x)-Laplace type operator with p(.) : Ω → [1, +∞) a measurable function and b a continuous and nondecreasing function from R → R. We prove the existence and uniqueness of an entropy solution for L 1 -data f .
In this paper, the limit behavior of nonlinear problems with nonhomogeneous Fourier boundary conditions, in a connected domain is established. This domain consists of two separate parts jointed by a set of bridges. The parameter describing the heterogeneities of the material and the size of the bridges can be very small. The homogenization method is used to estimate the field of temperatures attainable in the medium, depending of the relative order of the size of the bridges. Three situations are studied according to the connectedness of the components of the domain.
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